document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178476>Question 1178476</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to the American Society of Heating, Refrigerating<BR>\n" );
document.write( "and Air-Conditioning Engineers, Inc. (ASHRAE), a nonsmoking classroom<BR>\n" );
document.write( "should have a ventilation rate of 15 ft3 per min for each person in the room.<BR>\n" );
document.write( "(a) Write an equation that models the total ventilation V (in cubic feet per hour)<BR>\n" );
document.write( "necessary for a classroom with x students.<BR>\n" );
document.write( "(b) A common unit of ventilation is air change per hour (ach). One ach is equivalent<BR>\n" );
document.write( "to exchanging all the air in a room every hour. If x students are in a classroom<BR>\n" );
document.write( "having volume 15,000 ft3, determine how many air exchanges per hour (A) are<BR>\n" );
document.write( "necessary to keep the room properly ventilated.<BR>\n" );
document.write( "(c) Find the necessary number of ach (A) if the classroom has 40 students in it.<BR>\n" );
document.write( "(d) In areas like bars and lounges that allow smoking, the ventilation rate should<BR>\n" );
document.write( "be increased to 50 ft3 per min per person. Compared to classrooms, ventilation<BR>\n" );
document.write( "should be increased by what factor in heavy smoking areas? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850339 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this problem step by step:\r<BR>\n" );
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document.write( "**(a) Equation for Total Ventilation (V)**\r<BR>\n" );
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document.write( "* **Ventilation per person:** 15 ft³/min<BR>\n" );
document.write( "* **Number of students:** x<BR>\n" );
document.write( "* **Total ventilation per minute:** 15x ft³/min<BR>\n" );
document.write( "* **Convert to cubic feet per hour:** 15x ft³/min * 60 min/hour = 900x ft³/hour\r<BR>\n" );
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document.write( "Therefore, the equation is:<BR>\n" );
document.write( "* **V = 900x**\r<BR>\n" );
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document.write( "**(b) Air Exchanges per Hour (A)**\r<BR>\n" );
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document.write( "* **Total ventilation per hour:** V = 900x ft³/hour<BR>\n" );
document.write( "* **Classroom volume:** 15,000 ft³<BR>\n" );
document.write( "* **Air exchanges per hour (A):** A = (Total ventilation per hour) / (Classroom volume)<BR>\n" );
document.write( "* **A = (900x) / 15,000**<BR>\n" );
document.write( "* **A = 9x / 150 = 3x / 50**\r<BR>\n" );
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document.write( "Therefore, the number of air exchanges per hour is:<BR>\n" );
document.write( "* **A = 3x / 50**\r<BR>\n" );
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document.write( "**(c) Necessary Air Exchanges with 40 Students**\r<BR>\n" );
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document.write( "* **Number of students (x):** 40<BR>\n" );
document.write( "* **A = 3x / 50**<BR>\n" );
document.write( "* **A = 3(40) / 50**<BR>\n" );
document.write( "* **A = 120 / 50**<BR>\n" );
document.write( "* **A = 12 / 5 = 2.4**\r<BR>\n" );
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document.write( "Therefore, with 40 students, 2.4 air exchanges per hour are necessary.\r<BR>\n" );
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document.write( "**(d) Ventilation Increase in Smoking Areas**\r<BR>\n" );
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document.write( "* **Ventilation in classrooms:** 15 ft³/min per person<BR>\n" );
document.write( "* **Ventilation in smoking areas:** 50 ft³/min per person<BR>\n" );
document.write( "* **Factor increase:** (Ventilation in smoking areas) / (Ventilation in classrooms)<BR>\n" );
document.write( "* **Factor increase:** 50 / 15<BR>\n" );
document.write( "* **Factor increase:** 10 / 3 ≈ 3.33\r<BR>\n" );
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document.write( "Therefore, ventilation should be increased by a factor of 10/3 or approximately 3.33 in heavy smoking areas.<BR>\n" );
document.write( " </SPAN>\n" );
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